parallel_line_fusion_exp_4 <- function(N_schedule, time_schedule, start_beta, C_schedule, L, base_samples, study = F) {
if (length(N_schedule) != (L-1)) stop('length of N_schedule must be equal to (L-1)')
if (length(time_schedule) != (L-1)) stop('length of time_schedule must be equal to (L-1)')
if (length(C_schedule) == (L-1)) {
~ # check that at each level, we are fusing a suitable number
for (l in length(C_schedule):1) {
if (((1/start_beta)/prod(C_schedule[(L-1):l]))%%1 != 0) {
stop('check that (1/beta)/prod(C_schedule[(L-1):l]) is an integer for l=L-1,...,1')
}
}
} else {
stop('C_schedule must be a vector of length (L-1)')
}
# we append 1 to the vector C_schedule to make the indices work later on when we call fusion
# we need this so that we can set the right value for beta when fusing up the levels
C_schedule <- c(C_schedule, 1)
# initialising study results
hier_samples <- list()
hier_samples[[L]] <- base_samples # base level
time_taken_per_level <- rep(0, L-1)
input_betas <- list()
input_betas[[L]] <- NA
output_beta <- c(1:(L-1), start_beta)
# make some vectors for acceptance rates of the level
rho_acc <- rep(0, L-1)
Q_acc <- rep(0, L-1)
rhoQ_acc <- rep(0, L-1)
# creating parallel cluster
n_cores <- parallel::detectCores()
cl <- parallel::makeCluster(n_cores, outfile = 'parallel_line_fusion_exp_4.txt')
# creating variable and functions list to pass into cluster using clusterExport
varlist <- list("phi_function_exp_4", "bounds_phi_function_exp_4", "simulate_langevin_diffusion_exp_4",
"fusion_diff_exp_4", "N_schedule", "time_schedule", "start_beta", "C_schedule", "L", "base_samples")
parallel::clusterExport(cl, envir = environment(), varlist = varlist)
# exporting functions from layeredBB package to simulate layered Brownian bridges
parallel::clusterExport(cl, varlist = ls("package:layeredBB"))
# add to output file that starting hierarchical fusion
cat('Starting hierarchical fusion \n', file = 'parallel_line_fusion_exp_4.txt')
# parallelising tasks for each level going up the hiearchy
for (k in ((L-1):1)) {
samples_per_core <- rep(floor(N_schedule[k]/n_cores), n_cores)
if (sum(samples_per_core) != N_schedule[k]) {
remainder <- N_schedule[k] %% n_cores
samples_per_core[1:remainder] <- samples_per_core[1:remainder] + 1
}
# performing Fusion for this level
# printing out some stuff to log file to track the progress
cat('########################\n', file = 'parallel_line_fusion_exp_4.txt', append = T)
cat('Starting to fuse', C_schedule[k], 'densities of pi^beta, where beta =', prod(C_schedule[L:(k+1)]), '/',
(1/start_beta), 'for level', k, 'with time', time_schedule[k], ', which is using', n_cores, 'cores\n',
file = 'parallel_line_fusion_exp_4.txt', append = T)
cat('Obtaining', N_schedule[k], 'samples for beta =', prod(C_schedule[L:k]), '/', (1/start_beta),
'\n', file = 'parallel_line_fusion_exp_4.txt', append = T)
cat('########################\n', file = 'parallel_line_fusion_exp_4.txt', append = T)
# starting fusion
pcm <- proc.time()
fused <- parallel::parLapplyLB(cl, X = 1:length(samples_per_core), fun = function(i) {
fusion_diff_exp_4(N = samples_per_core[i],
time = time_schedule[k],
C = C_schedule[k],
samples_to_fuse = rep(list(hier_samples[[k+1]]), C_schedule[k]),
betas = prod(C_schedule[L:(k+1)])*(start_beta),
level = k,
acceptance_rate = TRUE)})
final <- proc.time() - pcm
# putting the fusion samples into hier_samples[[k]]
hier_samples[[k]] <- unlist(sapply(1:length(fused), function(i) fused[[i]]$samples))
if (study) {
# calculating the acceptance rates for all nodes in the current level
# summing all the iterations for each core
rho_iterations <- sum(sapply(1:length(fused), function(i) fused[[i]]$iters_rho))
Q_iterations <- sum(sapply(1:length(fused), function(i) fused[[i]]$iters_Q))
rho_acc[k] <- Q_iterations / rho_iterations
Q_acc[k] <- (N_schedule[k]) / Q_iterations
rhoQ_acc[k] <- (N_schedule[k]) / rho_iterations
time_taken_per_level[k] <- final['elapsed']
input_betas[[k]] <- rep(prod(C_schedule[L:(k+1)])*(start_beta), C_schedule[k])
output_beta[k] <- prod(C_schedule[L:k])*(start_beta)
}
}
# stopping cluster
parallel::stopCluster(cl)
# print completion
cat('Completed hierarchical fusion\n', file = 'parallel_line_fusion_exp_4.txt', append = T)
if (study) {
return(list('samples' = hier_samples, 'time' = time_taken_per_level,
'rho_acc' = rho_acc, 'Q_acc' = Q_acc, 'rhoQ_acc' = rhoQ_acc,
'input_betas' = input_betas, 'output_beta' = output_beta, 'diffusion_times' = time_schedule))
} else {
return(hier_samples)
}
}
parallel_line_fusion_TA_exp_4 <- function(N_schedule, global_T, start_beta, C_schedule, L, base_samples, study = F) {
if (length(N_schedule) != (L-1)) stop('length of N_schedule must be equal to (L-1)')
if (length(C_schedule) == (L-1)) {
# check that at each level, we are fusing a suitable number
for (l in length(C_schedule):1) {
if (((1/start_beta)/prod(C_schedule[(L-1):l]))%%1 != 0) {
stop('check that (1/beta)/prod(C_schedule[(L-1):l]) is an integer for l=L-1,...,1')
}
}
} else {
stop('C_schedule must be a vector of length (L-1)')
}
# change global_T by multiplying it by sqrt(start_beta)
global_T <- global_T*sqrt(start_beta)
# we append 1 to the vector C_schedule to make the indices work later on when we call fusion
# we need this so that we can set the right value for beta when fusing up the levels
C_schedule <- c(C_schedule, 1)
# initialising study results
hier_samples <- list()
hier_samples[[L]] <- base_samples # base level
time_taken_per_level <- rep(0, L-1)
input_betas <- list()
input_betas[[L]] <- NA
output_beta <- c(1:(L-1), start_beta)
diffusion_times <- list()
# make some vectors for acceptance rates of the level
rho_acc <- rep(0, L-1)
Q_acc <- rep(0, L-1)
rhoQ_acc <- rep(0, L-1)
# creating parallel cluster
n_cores <- parallel::detectCores()
cl <- parallel::makeCluster(n_cores, outfile = 'parallel_line_fusion_TA_exp_4.txt')
# creating variable and functions list to pass into cluster using clusterExport
varlist <- list("phi_function_exp_4", "bounds_phi_function_exp_4", "simulate_langevin_diffusion_exp_4",
"fusion_TA_exp_4", "N_schedule", "global_T", "start_beta", "C_schedule", "L", "base_samples")
parallel::clusterExport(cl, envir = environment(), varlist = varlist)
# exporting functions from layeredBB package to simulate layered Brownian bridges
parallel::clusterExport(cl, varlist = ls("package:layeredBB"))
# add to output file that starting hierarchical fusion
cat('Starting hierarchical fusion \n', file = 'parallel_line_fusion_TA_exp_4.txt')
# parallelising tasks for each level going up the hiearchy
for (k in ((L-1):1)) {
samples_per_core <- rep(floor(N_schedule[k]/n_cores), n_cores)
if (sum(samples_per_core) != N_schedule[k]) {
remainder <- N_schedule[k] %% n_cores
samples_per_core[1:remainder] <- samples_per_core[1:remainder] + 1
}
# performing Fusion for this level
# printing out some stuff to log file to track the progress
cat('########################\n', file = 'parallel_line_fusion_TA_exp_4.txt', append = T)
cat('Starting to fuse', C_schedule[k], 'densities of pi^beta, where beta =', prod(C_schedule[L:(k+1)]), '/',
(1/start_beta), 'for level', k, 'with time', global_T/sqrt(prod(C_schedule[L:(k+1)])*(start_beta)),
', which is using', n_cores, 'cores\n',
file = 'parallel_line_fusion_TA_exp_4.txt', append = T)
cat('Obtaining', N_schedule[k], 'samples for beta =', prod(C_schedule[L:k]), '/', (1/start_beta),
'\n', file = 'parallel_line_fusion_TA_exp_4.txt', append = T)
cat('########################\n', file = 'parallel_line_fusion_TA_exp_4.txt', append = T)
# starting fusion
pcm <- proc.time()
fused <- parallel::parLapplyLB(cl, X = 1:length(samples_per_core), fun = function(i) {
fusion_TA_exp_4(N = samples_per_core[i],
time = global_T,
C = C_schedule[k],
samples_to_fuse = rep(list(hier_samples[[k+1]]), C_schedule[k]),
betas = prod(C_schedule[L:(k+1)])*(start_beta),
sample_weights = sqrt(prod(C_schedule[L:(k+1)])*(start_beta)),
level = k,
acceptance_rate = TRUE)})
final <- proc.time() - pcm
# putting the fusion samples into hier_samples[[k]]
hier_samples[[k]] <- unlist(sapply(1:length(fused), function(i) fused[[i]]$samples))
if (study) {
# calculating the acceptance rates for all nodes in the current level
# summing all the iterations for each core
rho_iterations <- sum(sapply(1:length(fused), function(i) fused[[i]]$iters_rho))
Q_iterations <- sum(sapply(1:length(fused), function(i) fused[[i]]$iters_Q))
rho_acc[k] <- Q_iterations / rho_iterations
Q_acc[k] <- (N_schedule[k]) / Q_iterations
rhoQ_acc[k] <- (N_schedule[k]) / rho_iterations
time_taken_per_level[k] <- final['elapsed']
input_betas[[k]] <- rep(prod(C_schedule[L:(k+1)])*(start_beta), C_schedule[k])
output_beta[k] <- prod(C_schedule[L:k])*(start_beta)
diffusion_times[[k]] <- global_T / rep(sqrt(prod(C_schedule[L:(k+1)])*(start_beta)), C_schedule[k])
}
}
# stopping cluster
parallel::stopCluster(cl)
# print completion
cat('Completed hierarchical fusion\n', file = 'parallel_line_fusion_TA_exp_4.txt', append = T)
hier_samples[[1]] <- unlist(hier_samples[[1]])
if (study) {
return(list('samples' = hier_samples, 'time' = time_taken_per_level,
'rho_acc' = rho_acc, 'Q_acc' = Q_acc, 'rhoQ_acc' = rhoQ_acc,
'input_betas' = input_betas, 'output_beta' = output_beta, 'diffusion_times' = diffusion_times))
} else {
return(hier_samples)
}
}
######################################## examples ########################################
library(exp4Tempering)
# obtaining samples for target via rejection sampling
test_target_mc <- sample_from_fc(N = 10000, proposal_mean = 0, proposal_sd = 1, dominating_M = 1.35, beta = 1)
######################################## beta = 1/4
# samples for base level (4 nodes for normal hierarchical fusion, just the first node (input_samples1[[1]]) for line fusion)
input_samples1 <- base_rejection_sampler_exp_4(beta = 1/4, nsamples = 100000,
proposal_mean = 0, proposal_sd = 1.5, dominating_M = 1.4)
# regular hierarchical fusion
test1_standard <- parallel_h_fusion_exp_4(N_schedule = rep(10000, 2), time_schedule = rep(1, 2),
start_beta = 1/4, C_schedule = rep(2, 2), L = 3,
base_samples = input_samples1, study = T)
test1_TA <- parallel_h_fusion_TA_exp_4(N_schedule = rep(10000, 2), global_T = 1,
start_beta = 1/4, C_schedule = rep(2, 2), L = 3,
base_samples = input_samples1, study = T)
# line fusion
test1_line <- parallel_line_fusion_exp_4(N_schedule = rep(10000, 2), time_schedule = rep(1, 2),
start_beta = 1/4, C_schedule = rep(2, 2), L = 3,
base_samples = input_samples1[[1]], study = T)
test1_line_TA <- parallel_line_fusion_TA_exp_4(N_schedule = rep(10000, 2), global_T = 1,
start_beta = 1/4, C_schedule = rep(2, 2), L = 3,
base_samples = input_samples1[[1]], study = T)
# plot the densities from line fusion
curve(target_density_exp_4(x), -2.5, 2.5, ylim = c(0,1))
lines(density(test_target_mc), col = 'black')
lines(density(test1_line$samples[[1]]), col = 'green')
lines(density(test1_line_TA$samples[[1]]), col = 'blue')
# print differences in time between the standard approaches
print(test1_standard$time)
print(test1_line$time)
# print differences in time between the TA approaches
print(test1_TA$time)
print(test1_line_TA$time)
# print total variation from the samples to the true density
print(total_variation_true_exp_4(test_target_mc))
print(total_variation_true_exp_4(test1_standard$samples[[1]]))
print(total_variation_true_exp_4(test1_TA$samples[[1]]))
print(total_variation_true_exp_4(test1_line$samples[[1]]))
print(total_variation_true_exp_4(test1_line$samples[[1]]))
# acceptance rate plots
acceptance_rate_plots(hier1 = test1_standard, hier2 = test1_line, time = 1)
acceptance_rate_plots(hier1 = test1_TA, hier2 = test1_line_TA, time = 1)
######################################## beta = 1/8
# samples for base level (8 nodes for normal hierarchical fusion, just the first node (input_samples2[[1]]) for line fusion)
input_samples2 <- hmc_base_sampler_exp_4(beta = 1/8, nsamples = 100000, nchains = 8)
# regular hierarchical fusion
test2_standard <- parallel_h_fusion_exp_4(N_schedule = rep(10000, 3), time_schedule = rep(1, 3),
start_beta = 1/8, C_schedule = rep(2, 3), L = 4,
base_samples = input_samples2, study = T)
test2_TA <- parallel_h_fusion_TA_exp_4(N_schedule = rep(10000, 3), global_T = 1,
start_beta = 1/8, C_schedule = rep(2, 3), L = 4,
base_samples = input_samples2, study = T)
# line fusion
test2_line <- parallel_line_fusion_exp_4(N_schedule = rep(10000, 3), time_schedule = rep(1, 3),
start_beta = 1/8, C_schedule = rep(2, 3), L = 4,
base_samples = input_samples2[[1]], study = T)
test2_line_TA <- parallel_line_fusion_TA_exp_4(N_schedule = rep(10000, 3), global_T = 1,
start_beta = 1/8, C_schedule = rep(2, 3), L = 4,
base_samples = input_samples2[[1]], study = T)
# print differences in time between the standard approaches
print(test2_standard$time)
print(test2_line$time)
# print differences in time between the TA approaches
print(test2_TA$time)
print(test2_line_TA$time)
# print total variation from the samples to the true density
print(total_variation_true_exp_4(test_target_mc))
print(total_variation_true_exp_4(test2_standard$samples[[1]]))
print(total_variation_true_exp_4(test2_TA$samples[[1]]))
print(total_variation_true_exp_4(test2_line$samples[[1]]))
print(total_variation_true_exp_4(test2_line$samples[[1]]))
# plot the densities from line fusion
curve(target_density_exp_4(x), -2.5, 2.5, ylim = c(0,1))
lines(density(test_target_mc), col = 'black')
lines(density(test2_line$samples[[1]]), col = 'green')
lines(density(test2_line_TA$samples[[1]]), col = 'blue')
# acceptance rate plots
acceptance_rate_plots(hier1 = test2_standard, hier2 = test2_line, time = 1)
acceptance_rate_plots(hier1 = test2_TA, hier2 = test2_line_TA, time = 1)
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